The last thing that is sewn onto a button down shirt are the buttons and they arrived a few weeks ago. When companies manufacture overseas, particularly in China, the manufacturer sources everything, including garment labels, hang tags, fabric, buttons, and trims. American factories are cut and sew factories, which means that fashion companies must provide EVERYTHING except for the thread (unless it's silk or some other fancy, nonstandard thread). Sourcing and counting buttons and labels are time consuming, but it's good practice. If I decide to manufacture overseas, I can be specific (or send samples) of the trims and fabric that I want. Instead of going back and forth (time is money), I can say, "I want 400 gsm hang tags, 5.5cm x 9cm, hole punched top middle. Here's the proof for the design" or "I want 18L high quality resin black 4 hole buttons."
If you ever start a fashion company, I recommend staying in the USA in order to learn how to source and get a hands on experience on the production process. You will have more oversight and will, most importantly, know how much things cost. The cheap prices overseas and/or the ease of dealing with a middle man who will do everything for you are tempting but, if you don't know what you are doing or what things cost, you will get shoddy and/or overpriced products.